What a scale actually means and what we can do with it
depends on what its numbers represent. Numbers can be grouped into 4 types
or levels: nominal, ordinal, interval, and ratio. Nominal is the most simple,
and ratio the most sophisticated. Each level possesses the characteristics
of the preceding level, plus an additional quality.

Nominal

Nominal is hardly measurement. It refers to quality more
than quantity. A nominal level of measurement is simply a matter of distinguishing
by name, e.g., 1 = male, 2 = female. Even though we are using the numbers 1
and 2, they do not denote quantity. The binary category of 0 and 1 used for
computers is a nominal level of measurement. They are categories or classifications.
Nominal measurement is like using categorical levels of variables, described
in the Doing Scientific Research section of the Introduction module.

Ordinal refers to order in measurement. An ordinal scale
indicates direction, in addition to providing nominal information. Low/Medium/High;
or Faster/Slower are examples of ordinal levels of measurement. Ranking an
experience as a "nine" on a scale of 1 to 10 tells us that it was
higher than an experience ranked as a "six." Many psychological scales
or inventories are at the ordinal level of measurement.

Examples:

RANK: 1st place, 2nd place, ...
last place

LEVEL OF AGREEMENT: No, Maybe, Yes

POLITICAL ORIENTATION: Left, Center, Right

Ordinal time
of day - indicates direction or order of occurrence;
spacing between is uneven

Interval

Interval scales provide information about order, and also
possess equal intervals. From the previous example, if we knew that the distance
between 1 and 2 was the same as that between 7 and 8 on our 10-point rating
scale, then we would have an interval scale. An example of an interval scale
is temperature, either measured on a Fahrenheit or Celsius scale. A degree
represents the same underlying amount of heat, regardless of where it occurs
on the scale. Measured in Fahrenheit units, the difference between a temperature
of 46 and 42 is the same as the difference between 72 and 68. Equal-interval
scales of measurement can be devised for opinions and attitudes. Constructing
them involves an understanding of mathematical and statistical principles beyond
those covered in this course. But it is important to understand the different
levels of measurement when using and interpreting scales.

Examples:

TIME OF DAY on a 12-hour clock

POLITICAL ORIENTATION: Score on standardized scale
of political orientation

OTHER scales constructed so as to possess equal intervals

Interval time of day -
equal intervals; analog (12-hr.) clock, difference between 1 and 2 pm is
same as difference between 11 and 12 am

Ratio

In addition to possessing the qualities of nominal, ordinal,
and interval scales, a ratio scale has an absolute zero (a point where none
of the quality being measured exists). Using a ratio scale permits comparisons
such as being twice as high, or one-half as much. Reaction time (how long it
takes to respond to a signal of some sort) uses a ratio scale of measurement
-- time. Although an individual's reaction time is always greater than zero,
we conceptualize a zero point in time, and can state that a response of 24
milliseconds is twice as fast as a response time of 48 milliseconds.

Examples:

RULER: inches or centimeters

YEARS of work experience

INCOME: money earned last year

NUMBER of children

GPA: grade point average

Ratio -
24-hr. time has an absolute 0 (midnight); 14 o'clock is twice as long from
midnight as 7 o'clock

Applications

The level of measurement for a particular variable is
defined by the highest category that it achieves. For example, categorizing
someone as extroverted (outgoing) or introverted (shy) is nominal. If we categorize
people 1 = shy, 2 = neither shy nor outgoing, 3 = outgoing, then we have an
ordinal level of measurement. If we use a standardized measure of shyness (and
there are such inventories), we would probably assume the shyness variable
meets the standards of an interval level of measurement. As to whether or not
we might have a ratio scale of shyness, although we might be able to measure
zero shyness, it would be difficult to devise a scale where we would be comfortable
talking about someone's being 3 times as shy as someone else.

Measurement at the interval or ratio level
is desirable because we can use the more powerful statistical procedures available
for Means and Standard Deviations. To have this advantage, often ordinal data
are treated as though they were interval; for example, subjective ratings scales
(1 = terrible, 2= poor, 3 = fair, 4 = good, 5 = excellent). The scale probably
does not meet the requirement of equal intervals -- we don't know that the
difference between 2 (poor) and 3 (fair) is the same as the difference between
4 (good) and 5 (excellent). In order to take advantage of more powerful statistical
techniques, researchers often assume that the intervals are equal.